I don't think they would know much about each other in a week and that would be too soon for a relationship. There might be a mystery for Jace but I don't think it is realistic for Clary to fall for him straight away. I think them getting to know more each other would be more realistic since when you meet someone new, you would want to know more about them being friends with them let alone start a relationship with them.

Yeah I agree. I think they firstly need to sort out what is happening with Valentine before anything happens. I feel like they did that in the books and I am hoping they do that for the show.